The elements of the sparse vectors \(\left\lbrace \mathbf {x}^{(l)}, l= 1:L\right\rbrace \)  are drawn from a Bernoulli-Gaussian distribution, and the vectors share a common support. The number of measurement vectors is 5. The performance of the algorithms with ill-conditioned, correlated, non-zero mean and low-rank measurement matrices is shown in Fig. REF  (a)-(d), respectively. In this figure, we also include the performance of the direct extension of the conventional SBL algorithm to the MMV model (MSBL) [1]}  and support-oracle bound.
It can be seen from this figure that, when the deviation of the measurement matrices from the i.i.d. zero-mean Gaussian matrix is small, GGAMP-SBL (with \(3\times \)  true noise variance) and UAMP-SBL deliver similar performance, and both of them can approach the bound closely. MSBL works slightly worse than GGAMP-SBL and UAMP-SBL. However, when the deviation is relatively large, MSBL delivers slightly better performance but at high complexity. In most cases, UAMP-SBL and MSBL almost have the same performance, and can significantly outperform GGAMP-SBL. As an example, we show the average runtime of different algorithms in the case of ill-conditioned matrices in Fig. REF (e), blackwhere UAMP-SBL converges significantly faster than GGAMP-SBL and MSBL.
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